Generalized Policy Iteration Adaptive Dynamic Programming for Discrete-Time Nonlinear Systems
提出一种广义策略迭代算法，通过迭代求解离散时间非线性系统的最优控制问题，使值函数单调收敛到最优解，并用神经网络实现近似最优控制。
This paper is concerned with a novel generalized policy iteration algorithm for solving optimal control problems for discrete-time nonlinear systems. The idea is to use an iterative adaptive dynamic programming algorithm to obtain iterative control laws which make the iterative value functions converge to the optimum. Initialized by an admissible control law, it is shown that the iterative value functions are monotonically nonincreasing and converge to the optimal solution of Hamilton-Jacobi-Bellman equation, under the assumption that a perfect function approximation is employed. The admissibility property is analyzed, which shows that any of the iterative control laws can stabilize the nonlinear system. Neural networks are utilized to implement the generalized policy iteration algorithm, by approximating the iterative value function and computing the iterative control law, respectively, to achieve approximate optimal control. Finally, numerical examples are presented to verify the effectiveness of the present generalized policy iteration algorithm.